Question

The equation of a SHM of amplitude $a$ and angular frequency $\omega$ in which all distances are measured from one extreme position and time is taken to be zero at the other extreme position is

• A. $x=a \sin \omega t$
• B. $x=a \cos \omega t$
• C. $x=a-a \sin \omega t$
• D. $x=a+a \cos \omega t$

Answer 1

Answer: (D)

If SHM. starts from means position, then
$x_{0}=a \sin \left(\omega t+\theta_{0}\right)$
Now, $x=x_{0}-(-a) \Rightarrow x=x_{0}+a=a+a \sin \left(\omega+\theta_{0}\right)$
At $t=0, x=2a$
$\Rightarrow 2 a=a+a \sin \left(\omega(0)+\theta_{0}\right)$
$\Rightarrow \theta_{0}=\frac{\pi}{2}$ or $x=a+a \sin \left(\omega t+\frac{\pi}{2}\right)$
$\Rightarrow x=a+a \cos \omega t$